Move the heat pump. Or use sound deadening materials.

More information is necessary to adequately answer your question. If the heat pump is outside and the noise is coming through the wall, you need to determine if it's a fan or motor noise or just vibration. Both can be lubricated, but if the bearings are shot its another story.

The Goodman heat pump is outside and the noise only occurs inside the house. The heat pump sound is normal outside. While only the fan is running there is no noise inside. Any time the compressor is running the sound is very loud inside and can be heard throughout the house.

A heat pump is much like an air conditioner compressor working back words. The copper lines coming into the home must be secured tightly with an insulating foam inside the clamp. Reach up and tough the copper line, can you feel it vibrate, does holding it tight deaden the sound slightly? If so, you are a candidate for more clamps.